524 Lord Rayleigh on the 



half to the upper half of the square, the progress from points 

 in the neighbourhood is always towards the point of inter- 

 section, so that the state represented thereby is stable. We 

 may sum up by saying that if, as the liquid strengthens, the 

 vapour having been weaker than the liquid becomes the 

 stronger, the point of transition, representing constant dis- 

 tillation, is stable; but if the vapour having been at first the 

 stronger becomes the weaker, then the point of transition is 

 unstable. 



The question presents itself, whether as the liquid strengthens 

 (in a particular ingredient) the vapour necessarily strengthens 

 with it. Does the curve on our diagram slope everywhere 

 upwards on its course from A to D ? Although a formal proof 

 may be lacking, it would seem probable that this must be so 

 when the ingredients mix in all proportions. A limiting case 

 is when two ingredients do not mix at all, e. g., water and 

 bisulphide of carbon, or when the mixture divides itself into 

 two parts of constant composition as when ether and water 

 are associated in certain proportions. In these cases the 

 composition of the vapour is constant for the whole or for a 

 part of the range (Konowalow), and the representative curve 

 is without slope. 



Konowalow's Theorem. 



An important connexion has been formulated by Kono- 

 walow* between the vapour- pressure, regarded as a function 

 of the composition of the liquid with which it is in equili- 

 brium, and the existence of a point of constant distillation. 

 " The pressure of the vapour from a fluid consisting of two 

 different substances is in general a function of the com- 

 position of the mixture... Let such a mixture, confined in 

 a closed space, be maintained at a constant temperature. 

 We may conceive this space bounded by fixed walls and by a 

 movable piston. The conditions of stable equilibrium are 

 then (1) that the external pressure operative upon the piston 

 should be equal to the pressure of the saturated vapour at the 

 given temperature ; (2) that by increase, or diminution, of 

 the vapour space the pressure should become respectively not 

 greater, or not less, than the external pressure. In expansion 

 the vapour-pressure can thus either remain constant, or be- 

 come smaller. On the basis of this law we can establish a 

 relation between the composition of the liquid and that of 

 the vapour/' 



Before proceeding further I must remark that the principle, 

 as stated, appears to need elucidation. Why should the 

 * Wied. Ann. xiv. p. 48 (1881). 



